## A police cruiser is traveling at 20.0 m/s when the officer spies a speeder. The cruiser accelerates at 3.0 m/s^2 for 5.0 seconds, at which t

Question

A police cruiser is traveling at 20.0 m/s when the officer spies a speeder. The cruiser accelerates at 3.0 m/s^2 for 5.0 seconds, at which time the speeder pulls over and starts thinking up excuses to try and get out of a ticket. The cruiser then slows to a stop at 5.0 m/s^2. How far does it go in the entire time?

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Math
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2022-02-02T06:42:36+00:00
2022-02-02T06:42:36+00:00 1 Answer
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## Answers ( )

For the first 5.0 seconds, the cruiser covers a distance of

[tex]\left(20.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2=137.5\,\mathrm m[/tex]

At this point, the cruiser will have achieved a velocity of

[tex]\left(20.0\dfrac{\rm m}{\rm s}\right)+\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)=35\dfrac{\rm m}{\rm s}[/tex]

The cruiser will take

[tex]\left(35\dfrac{\rm m}{\rm s}\right)-\left(5.0\dfrac{\rm m}{\mathrm s^2}\right)t=0\implies t=7.0\,\mathrm s[/tex]

to come to a stop as it decelerates. It will have covered a total distance of

[tex](137.5\,\mathrm m)+\left(35\dfrac{\rm m}{\rm s}\right)(7.0\,\mathrm s)+\dfrac12\left(-5.0\dfrac{\rm m}{\mathrm s^2}\right)(7.0\,\mathrm s)^2=\boxed{260\,\mathrm m}[/tex]